King Abdullah of Saudi Arabia, pictured in Jeddah last year. Photograph: Getty Images

Barack Obama took time out from his hectic schedule at the G20 summit in London to hold a brief bilateral meeting with King Abdullah of Saudi Arabia.

It was an encounter that passed with little media attention, apart from conservative outrage in the US that the president appeared to bow slightly when he met the monarch.

Discretion suited both sides, although the White House did reveal that the agenda included the global economy, terrorism, and the faltering Middle East peace process.

Whether there was any discussion of the highly delicate matter of Abdullah's eventual heir is not known.

The 86-year-old Abdullah rarely travels abroad, and when he does he makes sure there is someone left at home to mind the world's biggest oil exporter.

So shortly before leaving Riyadh for the Arab summit in Qatar and then the G20 in London, it was announced that his half-brother, Prince Nayef – no stripling at 75 – was to be appointed as the second deputy prime minister.

Both the title and circumstances need decoding: in the Saudi system, the king, always referred to as "the custodian of the two holy mosques", is prime minister and the crown prince the first deputy prime minister.

So the second deputy is likely to be the next crown prince and heir apparent.

Sultan, the current crown prince, is 85. He has been abroad since November, is suffering from cancer and is recuperating from an operation in New York.

That meant that the technical-sounding news about Nayef's new job was something of a bombshell because it implied he was next in line for the throne.

Taking into account the advanced ages of both Abdullah and Sultan, he could be sitting on it sooner rather than later.

Experts point out that this is not certain. Formally, the choice is down to a secretive body called the Allegiance council, set up in 2006 and made up of the most prominent members of the royal family (all the sons or grandsons of the late King Abdulaziz, or Ibn Saud, the founder of the kingdom), who vote to appoint crown princes.

Gregory Gause, of the University of Vermont, calls this a "wild card" in the succession process.

Other Saudi-watchers predict that Nayef will eventually take over.

"The question is still open but, most probably, Nayef will be king," Mai Yamani, a London-based Saudi political analyst, said. "He is too powerful to be ignored."

Nayef's claim to fame is more than 30 years of service as the interior minister.

He organised the attack that ended the traumatic siege of the Grand Mosque in Mecca 1979, and has led the fight against al-Qaida since the 9/11 attacks (having first blamed Israel's Mossad and denied that any Saudis were involved).

Brute force has been combined with a sophisticated rehabilitation programme to coax repentant "deviants" or jihadis back into the fold.

With his son, Prince Mohammed, as the deputy minister, Nayef runs a classic and powerful Saudi fiefdom.

He is also a social conservative who declared, days before his appointment, that there was no need for either elections or for female members of the advisory Shura council.

Nayef rarely travels overseas, and is one of the few Saudi princes never to have visited Washington.

Reformists who have hailed some cautious changes under Abdullah, including the recent appointment of the kingdom's first woman minister, are understandably dismayed.

It all highlights why the succession is such a sensitive issue in a country that places a high premium on stability, and where the crown has passed horizontally from brother to brother for more than half a century.

That means vertical change – to a new generation – could bring the threat of uncontrollable rivalry because of the sheer number of princes hoping to inherit their fathers' position and patronage.

Nervous adherence to the status quo is why the Saudi media has been dutifully reporting that Abdullah, and especially Sultan, are in good health.

At the same time, it has praised Nayef for – in the words of one characteristically sycophantic newspaper – having the "experience, political skills and integrity" required to assume the leadership of the country.

"This is an impenetrable system based on the whims of princes and their internal politics," Madawi al-Rasheed, a London University expert on the kingdom, said.

"It's basically about what they can get away with."

Nayef also has a reputation for being fiercely anti-Shia, cracking down on the minority in the Eastern province.

He is also more hawkishly anti-Iranian than the accommodating Abdullah. This could create complications as Obama seeks to engage with Tehran and its nuclear ambitions and grapples with what could be the defining foreign policy issue of his presidency.

Amid such conflicting assessments, critics say the way the succession is being handled is typical of an unaccountable system that operates in its own interests - another example, for al-Rasheed, of "desperate attempts to save the House of Saud, not from jihadi violence, reformers' pressure or external threats but from the hazards of demography and natural ageing."

Or as the politicial analyst Mai Yamani puts it: "The only thing that changes the ruler in our part of the world is death."